Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: It is proved that the filter can control the total variation of the solution and also produce sharp discrete shocks in a nonlinear conservation form filter.
Abstract: A new type of methods for the numerical approximation of hyperbolic conservation laws with discontinuous solution is introduced. The methods are based on standard finite difference schemes. The difference solution is processed with a nonlinear conservation form filter at every time level to eliminate spurious oscillations near shocks. It is proved that the filter can control the total variation of the solution and also produce sharp discrete shocks. The method is simpler and faster than many other high resolution schemes for shock calculations. Numerical examples in one and two space dimensions are presented.
99 citations
TL;DR: In this article, the authors reformulate the existing auxiliary differential equation (ADE) technique in the context of the finite-difference time-domain analysis of Maxwell's equations for the modeling of optical pulse propagation in linear Lorentz and nonlinear Kerr and Raman media.
Abstract: We reformulate the existing auxiliary differential equation (ADE) technique in the context of the finite-difference time-domain analysis of Maxwell's equations for the modeling of optical pulse propagation in linear Lorentz and nonlinear Kerr and Raman media. Our formulation is based on the polarization terms and allows simple and consistent implementation of such media together with the anisotropic perfectly matched layer (APML) absorbing boundary condition. The disadvantages of the ADE technique, i.e., requiring additional storage for auxiliary variables, has been overcome by adopting the high-order finite-difference schemes derived from the previously reported wavelet-based formulation. With those techniques, we demonstrate in two-dimensional setting an effective and accurate numerical analysis of the spatio-temporal soliton propagation as a consequence of the physically originated balanced phenomena between the self-focusing effect of nonlinearity and the pulse broadening effects of the temporal dispersion and of the spatial diffraction.
99 citations
TL;DR: In this paper, a technique for solving the finite difference biharmonic equation as a coupled pair of harmonic difference equations is proposed, which is a general block SOR method with convergence rate O(h^(h 1 / 2 )$ on a square, where h is mesh size.
Abstract: A technique is proposed for solving the finite difference biharmonic equation as a coupled pair of harmonic difference equations. Essentially, the method is a general block SOR method with convergence rate $O(h^{{1 / 2}} )$ on a square, where h is mesh size.
99 citations
TL;DR: In this article, a new family of implicit, single-step time integration methods is presented for solving structural dynamics problems, which are unconditionally stable, second-order accurate and asymptotically annihilating.
99 citations
TL;DR: Numerical comparisons with pure finite-difference methods demonstrate the effectiveness of techniques that combine grid and particle solvers for the solution of the incompressible Navier--Stokes equations for various flow geometries, bounded or unbounded.
Abstract: We describe and illustrate numerical procedures that combine grid and particle solvers for the solution of the incompressible Navier--Stokes equations. These procedures include vortex in cell (VIC) and domain decomposition schemes. Numerical comparisons with pure finite-difference methods demonstrate the effectiveness of these techniques for various flow geometries, bounded or unbounded.
98 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |